LMFDB - Embedded newform 1680.2.bg.o.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1680.961
Dual form			1680.2.bg.o.1201.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{11} +2.26795 q^{13} +1.00000 q^{15} +(-1.63397 - 2.83013i) q^{17} +(2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +(-2.36603 + 4.09808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -4.19615 q^{29} +(-0.232051 - 0.401924i) q^{31} +(0.366025 - 0.633975i) q^{33} +(2.59808 + 0.500000i) q^{35} +(1.59808 - 2.76795i) q^{37} +(-1.13397 - 1.96410i) q^{39} -0.732051 q^{41} -3.19615 q^{43} +(-0.500000 - 0.866025i) q^{45} +(1.00000 - 1.73205i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-1.63397 + 2.83013i) q^{51} +(-6.19615 - 10.7321i) q^{53} -0.732051 q^{55} -4.46410 q^{57} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(2.59808 + 0.500000i) q^{63} +(-1.13397 + 1.96410i) q^{65} +(-7.33013 - 12.6962i) q^{67} +4.73205 q^{69} -6.19615 q^{71} +(-6.33013 - 10.9641i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(1.26795 - 1.46410i) q^{77} +(-3.69615 + 6.40192i) q^{79} +(-0.500000 - 0.866025i) q^{81} -15.1244 q^{83} +3.26795 q^{85} +(2.09808 + 3.63397i) q^{87} +(-7.56218 + 13.0981i) q^{89} +(-1.96410 - 5.66987i) q^{91} +(-0.232051 + 0.401924i) q^{93} +(2.23205 + 3.86603i) q^{95} +14.9282 q^{97} -0.732051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} + 16 q^{13} + 4 q^{15} - 10 q^{17} + 2 q^{19} - 6 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} + 6 q^{31} - 2 q^{33} - 4 q^{37} - 8 q^{39} + 4 q^{41} + 8 q^{43} - 2 q^{45} + 4 q^{47} - 22 q^{49} - 10 q^{51} - 4 q^{53} + 4 q^{55} - 4 q^{57} + 10 q^{59} - 8 q^{61} - 8 q^{65} - 12 q^{67} + 12 q^{69} - 4 q^{71} - 8 q^{73} - 2 q^{75} + 12 q^{77} + 6 q^{79} - 2 q^{81} - 12 q^{83} + 20 q^{85} - 2 q^{87} - 6 q^{89} + 6 q^{91} + 6 q^{93} + 2 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 - 2 * q^11 + 16 * q^13 + 4 * q^15 - 10 * q^17 + 2 * q^19 - 6 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 + 6 * q^31 - 2 * q^33 - 4 * q^37 - 8 * q^39 + 4 * q^41 + 8 * q^43 - 2 * q^45 + 4 * q^47 - 22 * q^49 - 10 * q^51 - 4 * q^53 + 4 * q^55 - 4 * q^57 + 10 * q^59 - 8 * q^61 - 8 * q^65 - 12 * q^67 + 12 * q^69 - 4 * q^71 - 8 * q^73 - 2 * q^75 + 12 * q^77 + 6 * q^79 - 2 * q^81 - 12 * q^83 + 20 * q^85 - 2 * q^87 - 6 * q^89 + 6 * q^91 + 6 * q^93 + 2 * q^95 + 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	0.915916	−	0.401371i	$-0.131466\pi$
$11$	0.366025	+	0.633975i	0.110361	+	0.191151i	−0.805555	+	0.592521i	$0.798133\pi$
$12$		0			0
$13$	2.26795			0.629016			0.314508	−	0.949255i	$-0.398160\pi$
$13$	2.26795			0.629016			0.314508	+	0.949255i	$0.398160\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−1.63397	−	2.83013i	−0.396297	−	0.686407i	0.596969	−	0.802264i	$-0.296372\pi$
$17$	−1.63397	−	2.83013i	−0.396297	−	0.686407i	−0.993266	+	0.115858i	$0.963038\pi$
$18$		0			0
$19$	2.23205	−	3.86603i	0.512068	−	0.886927i	−0.487835	−	0.872936i	$-0.662213\pi$
$19$	2.23205	−	3.86603i	0.512068	−	0.886927i	0.999902	−	0.0139909i	$-0.00445360\pi$
$20$		0			0
$21$	−1.73205	+	2.00000i	−0.377964	+	0.436436i
$22$		0			0
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	−0.999971	−	0.00766135i	$-0.997561\pi$
$23$	−2.36603	+	4.09808i	−0.493350	+	0.854508i	0.506620	+	0.862169i	$0.330895\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−4.19615			−0.779206			−0.389603	−	0.920983i	$-0.627388\pi$
$29$	−4.19615			−0.779206			−0.389603	+	0.920983i	$0.627388\pi$
$30$		0			0
$31$	−0.232051	−	0.401924i	−0.0416776	−	0.0721876i	0.844434	−	0.535659i	$-0.179937\pi$
$31$	−0.232051	−	0.401924i	−0.0416776	−	0.0721876i	−0.886112	+	0.463472i	$0.846604\pi$
$32$		0			0
$33$	0.366025	−	0.633975i	0.0637168	−	0.110361i
$34$		0			0
$35$	2.59808	+	0.500000i	0.439155	+	0.0845154i
$36$		0			0
$37$	1.59808	−	2.76795i	0.262722	−	0.455048i	−0.704242	−	0.709960i	$-0.748713\pi$
$37$	1.59808	−	2.76795i	0.262722	−	0.455048i	0.966964	+	0.254912i	$0.0820464\pi$
$38$		0			0
$39$	−1.13397	−	1.96410i	−0.181581	−	0.314508i
$40$		0			0
$41$	−0.732051			−0.114327			−0.0571636	−	0.998365i	$-0.518206\pi$
$41$	−0.732051			−0.114327			−0.0571636	+	0.998365i	$0.518206\pi$
$42$		0			0
$43$	−3.19615			−0.487409			−0.243704	−	0.969850i	$-0.578363\pi$
$43$	−3.19615			−0.487409			−0.243704	+	0.969850i	$0.578363\pi$
$44$		0			0
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$		0			0
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	−1.63397	+	2.83013i	−0.228802	+	0.396297i
$52$		0			0
$53$	−6.19615	−	10.7321i	−0.851107	−	1.47416i	−0.880210	−	0.474584i	$-0.842598\pi$
$53$	−6.19615	−	10.7321i	−0.851107	−	1.47416i	0.0291032	−	0.999576i	$-0.490735\pi$
$54$		0			0
$55$	−0.732051			−0.0987097
$56$		0			0
$57$	−4.46410			−0.591285
$58$		0			0
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	0.859571	−	0.511017i	$-0.170731\pi$
$59$	−0.0980762	−	0.169873i	−0.0127684	−	0.0221156i	−0.872339	+	0.488901i	$0.837398\pi$
$60$		0			0
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	−0.965187	−	0.261562i	$-0.915762\pi$
$61$	−2.00000	+	3.46410i	−0.256074	+	0.443533i	0.709113	+	0.705095i	$0.249096\pi$
$62$		0			0
$63$	2.59808	+	0.500000i	0.327327	+	0.0629941i
$64$		0			0
$65$	−1.13397	+	1.96410i	−0.140652	+	0.243617i
$66$		0			0
$67$	−7.33013	−	12.6962i	−0.895518	−	1.55108i	−0.833163	−	0.553028i	$-0.813472\pi$
$67$	−7.33013	−	12.6962i	−0.895518	−	1.55108i	−0.0623548	−	0.998054i	$-0.519861\pi$
$68$		0			0
$69$	4.73205			0.569672
$70$		0			0
$71$	−6.19615			−0.735348			−0.367674	−	0.929955i	$-0.619846\pi$
$71$	−6.19615			−0.735348			−0.367674	+	0.929955i	$0.619846\pi$
$72$		0			0
$73$	−6.33013	−	10.9641i	−0.740885	−	1.28325i	−0.952093	−	0.305810i	$-0.901073\pi$
$73$	−6.33013	−	10.9641i	−0.740885	−	1.28325i	0.211207	−	0.977441i	$-0.432260\pi$
$74$		0			0
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$		0			0
$77$	1.26795	−	1.46410i	0.144496	−	0.166850i
$78$		0			0
$79$	−3.69615	+	6.40192i	−0.415850	+	0.720273i	−0.995517	−	0.0945803i	$-0.969849\pi$
$79$	−3.69615	+	6.40192i	−0.415850	+	0.720273i	0.579668	+	0.814853i	$0.303182\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−15.1244			−1.66011			−0.830057	−	0.557679i	$-0.811692\pi$
$83$	−15.1244			−1.66011			−0.830057	+	0.557679i	$0.811692\pi$
$84$		0			0
$85$	3.26795			0.354459
$86$		0			0
$87$	2.09808	+	3.63397i	0.224937	+	0.389603i
$88$		0			0
$89$	−7.56218	+	13.0981i	−0.801589	+	1.38839i	0.116980	+	0.993134i	$0.462679\pi$
$89$	−7.56218	+	13.0981i	−0.801589	+	1.38839i	−0.918570	+	0.395259i	$0.870655\pi$
$90$		0			0
$91$	−1.96410	−	5.66987i	−0.205894	−	0.594364i
$92$		0			0
$93$	−0.232051	+	0.401924i	−0.0240625	+	0.0416776i
$94$		0			0
$95$	2.23205	+	3.86603i	0.229004	+	0.396646i
$96$		0			0
$97$	14.9282			1.51573			0.757865	−	0.652412i	$-0.226243\pi$
$97$	14.9282			1.51573			0.757865	+	0.652412i	$0.226243\pi$
$98$		0			0
$99$	−0.732051			−0.0735739
$100$		0			0
$101$	3.63397	+	6.29423i	0.361594	+	0.626299i	0.988223	−	0.153018i	$-0.0488993\pi$
$101$	3.63397	+	6.29423i	0.361594	+	0.626299i	−0.626629	+	0.779317i	$0.715566\pi$
$102$		0			0
$103$	−4.59808	+	7.96410i	−0.453062	+	0.784726i	−0.998574	−	0.0533764i	$-0.983002\pi$
$103$	−4.59808	+	7.96410i	−0.453062	+	0.784726i	0.545513	+	0.838103i	$0.316335\pi$
$104$		0			0
$105$	−0.866025	−	2.50000i	−0.0845154	−	0.243975i
$106$		0			0
$107$	1.09808	−	1.90192i	0.106155	−	0.183866i	−0.808054	−	0.589108i	$-0.799479\pi$
$107$	1.09808	−	1.90192i	0.106155	−	0.183866i	0.914210	+	0.405242i	$0.132813\pi$
$108$		0			0
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$		0			0
$111$	−3.19615			−0.303365
$112$		0			0
$113$	8.92820			0.839895			0.419947	−	0.907548i	$-0.362049\pi$
$113$	8.92820			0.839895			0.419947	+	0.907548i	$0.362049\pi$
$114$		0			0
$115$	−2.36603	−	4.09808i	−0.220633	−	0.382148i
$116$		0			0
$117$	−1.13397	+	1.96410i	−0.104836	+	0.181581i
$118$		0			0
$119$	−5.66025	+	6.53590i	−0.518875	+	0.599145i
$120$		0			0
$121$	5.23205	−	9.06218i	0.475641	−	0.823834i
$122$		0			0
$123$	0.366025	+	0.633975i	0.0330034	+	0.0571636i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−4.80385			−0.426273			−0.213136	−	0.977022i	$-0.568368\pi$
$127$	−4.80385			−0.426273			−0.213136	+	0.977022i	$0.568368\pi$
$128$		0			0
$129$	1.59808	+	2.76795i	0.140703	+	0.243704i
$130$		0			0
$131$	7.73205	−	13.3923i	0.675552	−	1.17009i	−0.300755	−	0.953702i	$-0.597239\pi$
$131$	7.73205	−	13.3923i	0.675552	−	1.17009i	0.976307	−	0.216390i	$-0.0694281\pi$
$132$		0			0
$133$	−11.5981	−	2.23205i	−1.00568	−	0.193543i
$134$		0			0
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$		0			0
$137$	−1.09808	−	1.90192i	−0.0938150	−	0.162492i	0.815298	−	0.579041i	$-0.196573\pi$
$137$	−1.09808	−	1.90192i	−0.0938150	−	0.162492i	−0.909113	+	0.416549i	$0.863240\pi$
$138$		0			0
$139$	−5.92820			−0.502824			−0.251412	−	0.967880i	$-0.580895\pi$
$139$	−5.92820			−0.502824			−0.251412	+	0.967880i	$0.580895\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	0.830127	+	1.43782i	0.0694187	+	0.120237i
$144$		0			0
$145$	2.09808	−	3.63397i	0.174236	−	0.301785i
$146$		0			0
$147$	6.50000	+	2.59808i	0.536111	+	0.214286i
$148$		0			0
$149$	−2.92820	+	5.07180i	−0.239888	+	0.415498i	−0.960682	−	0.277651i	$-0.910444\pi$
$149$	−2.92820	+	5.07180i	−0.239888	+	0.415498i	0.720794	+	0.693149i	$0.243777\pi$
$150$		0			0
$151$	−4.46410	−	7.73205i	−0.363283	−	0.629225i	0.625216	−	0.780452i	$-0.285011\pi$
$151$	−4.46410	−	7.73205i	−0.363283	−	0.629225i	−0.988499	+	0.151227i	$0.951678\pi$
$152$		0			0
$153$	3.26795			0.264198
$154$		0			0
$155$	0.464102			0.0372775
$156$		0			0
$157$	−3.19615	−	5.53590i	−0.255081	−	0.441813i	0.709837	−	0.704366i	$-0.248769\pi$
$157$	−3.19615	−	5.53590i	−0.255081	−	0.441813i	−0.964917	+	0.262553i	$0.915435\pi$
$158$		0			0
$159$	−6.19615	+	10.7321i	−0.491387	+	0.851107i
$160$		0			0
$161$	12.2942	+	2.36603i	0.968921	+	0.186469i
$162$		0			0
$163$	10.9282	−	18.9282i	0.855963	−	1.48257i	−0.0197859	−	0.999804i	$-0.506298\pi$
$163$	10.9282	−	18.9282i	0.855963	−	1.48257i	0.875749	−	0.482767i	$-0.160368\pi$
$164$		0			0
$165$	0.366025	+	0.633975i	0.0284950	+	0.0493549i
$166$		0			0
$167$	17.6603			1.36659			0.683296	−	0.730142i	$-0.260546\pi$
$167$	17.6603			1.36659			0.683296	+	0.730142i	$0.260546\pi$
$168$		0			0
$169$	−7.85641			−0.604339
$170$		0			0
$171$	2.23205	+	3.86603i	0.170689	+	0.295642i
$172$		0			0
$173$	−7.26795	+	12.5885i	−0.552572	+	0.957083i	0.445516	+	0.895274i	$0.353020\pi$
$173$	−7.26795	+	12.5885i	−0.552572	+	0.957083i	−0.998088	+	0.0618087i	$0.980313\pi$
$174$		0			0
$175$	−1.73205	+	2.00000i	−0.130931	+	0.151186i
$176$		0			0
$177$	−0.0980762	+	0.169873i	−0.00737186	+	0.0127684i
$178$		0			0
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	0.616417	−	0.787420i	$-0.288584\pi$
$179$	−5.00000	−	8.66025i	−0.373718	−	0.647298i	−0.990134	+	0.140122i	$0.955250\pi$
$180$		0			0
$181$	−24.3205			−1.80773			−0.903865	−	0.427819i	$-0.859282\pi$
$181$	−24.3205			−1.80773			−0.903865	+	0.427819i	$0.859282\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$		0			0
$185$	1.59808	+	2.76795i	0.117493	+	0.203504i
$186$		0			0
$187$	1.19615	−	2.07180i	0.0874713	−	0.151505i
$188$		0			0
$189$	−0.866025	−	2.50000i	−0.0629941	−	0.181848i
$190$		0			0
$191$	−4.46410	+	7.73205i	−0.323011	+	0.559472i	−0.981108	−	0.193462i	$-0.938028\pi$
$191$	−4.46410	+	7.73205i	−0.323011	+	0.559472i	0.658097	+	0.752933i	$0.271362\pi$
$192$		0			0
$193$	−0.598076	−	1.03590i	−0.0430505	−	0.0745656i	0.843697	−	0.536819i	$-0.180374\pi$
$193$	−0.598076	−	1.03590i	−0.0430505	−	0.0745656i	−0.886748	+	0.462254i	$0.847041\pi$
$194$		0			0
$195$	2.26795			0.162411
$196$		0			0
$197$	−0.339746			−0.0242059			−0.0121029	−	0.999927i	$-0.503853\pi$
$197$	−0.339746			−0.0242059			−0.0121029	+	0.999927i	$0.503853\pi$
$198$		0			0
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	0.932075	+	0.362267i	$0.117997\pi$
$199$	11.0000	+	19.0526i	0.779769	+	1.35060i	−0.152305	+	0.988334i	$0.548670\pi$
$200$		0			0
$201$	−7.33013	+	12.6962i	−0.517027	+	0.895518i
$202$		0			0
$203$	3.63397	+	10.4904i	0.255055	+	0.736280i
$204$		0			0
$205$	0.366025	−	0.633975i	0.0255643	−	0.0442787i
$206$		0			0
$207$	−2.36603	−	4.09808i	−0.164450	−	0.284836i
$208$		0			0
$209$	3.26795			0.226049
$210$		0			0
$211$	−7.07180			−0.486843			−0.243421	−	0.969921i	$-0.578270\pi$
$211$	−7.07180			−0.486843			−0.243421	+	0.969921i	$0.578270\pi$
$212$		0			0
$213$	3.09808	+	5.36603i	0.212277	+	0.367674i
$214$		0			0
$215$	1.59808	−	2.76795i	0.108988	−	0.188773i
$216$		0			0
$217$	−0.803848	+	0.928203i	−0.0545687	+	0.0630105i
$218$		0			0
$219$	−6.33013	+	10.9641i	−0.427750	+	0.740885i
$220$		0			0
$221$	−3.70577	−	6.41858i	−0.249277	−	0.431761i
$222$		0			0
$223$	20.3923			1.36557			0.682785	−	0.730619i	$-0.260769\pi$
$223$	20.3923			1.36557			0.682785	+	0.730619i	$0.260769\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	−0.830127	−	1.43782i	−0.0550975	−	0.0954316i	0.837161	−	0.546956i	$-0.184214\pi$
$227$	−0.830127	−	1.43782i	−0.0550975	−	0.0954316i	−0.892259	+	0.451525i	$0.850880\pi$
$228$		0			0
$229$	1.50000	−	2.59808i	0.0991228	−	0.171686i	−0.812199	−	0.583380i	$-0.801730\pi$
$229$	1.50000	−	2.59808i	0.0991228	−	0.171686i	0.911322	+	0.411695i	$0.135063\pi$
$230$		0			0
$231$	−1.90192	−	0.366025i	−0.125137	−	0.0240827i
$232$		0			0
$233$	−8.66025	+	15.0000i	−0.567352	+	0.982683i	0.429474	+	0.903079i	$0.358699\pi$
$233$	−8.66025	+	15.0000i	−0.567352	+	0.982683i	−0.996827	+	0.0796037i	$0.974635\pi$
$234$		0			0
$235$	1.00000	+	1.73205i	0.0652328	+	0.112987i
$236$		0			0
$237$	7.39230			0.480182
$238$		0			0
$239$	−7.07180			−0.457437			−0.228718	−	0.973493i	$-0.573453\pi$
$239$	−7.07180			−0.457437			−0.228718	+	0.973493i	$0.573453\pi$
$240$		0			0
$241$	−6.73205	−	11.6603i	−0.433650	−	0.751103i	0.563535	−	0.826092i	$-0.309441\pi$
$241$	−6.73205	−	11.6603i	−0.433650	−	0.751103i	−0.997184	+	0.0749893i	$0.976108\pi$
$242$		0			0
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−1.00000	−	6.92820i	−0.0638877	−	0.442627i
$246$		0			0
$247$	5.06218	−	8.76795i	0.322099	−	0.557891i
$248$		0			0
$249$	7.56218	+	13.0981i	0.479234	+	0.830057i
$250$		0			0
$251$	24.5885			1.55201			0.776005	−	0.630727i	$-0.217243\pi$
$251$	24.5885			1.55201			0.776005	+	0.630727i	$0.217243\pi$
$252$		0			0
$253$	−3.46410			−0.217786
$254$		0			0
$255$	−1.63397	−	2.83013i	−0.102323	−	0.177229i
$256$		0			0
$257$	2.83013	−	4.90192i	0.176538	−	0.305774i	−0.764154	−	0.645034i	$-0.776843\pi$
$257$	2.83013	−	4.90192i	0.176538	−	0.305774i	0.940693	+	0.339260i	$0.110177\pi$
$258$		0			0
$259$	−8.30385	−	1.59808i	−0.515976	−	0.0992996i
$260$		0			0
$261$	2.09808	−	3.63397i	0.129868	−	0.224937i
$262$		0			0
$263$	4.19615	+	7.26795i	0.258746	+	0.448161i	0.965906	−	0.258892i	$-0.0833575\pi$
$263$	4.19615	+	7.26795i	0.258746	+	0.448161i	−0.707160	+	0.707053i	$0.750024\pi$
$264$		0			0
$265$	12.3923			0.761253
$266$		0			0
$267$	15.1244			0.925596
$268$		0			0
$269$	6.26795	+	10.8564i	0.382164	+	0.661927i	0.991371	−	0.131084i	$-0.0418457\pi$
$269$	6.26795	+	10.8564i	0.382164	+	0.661927i	−0.609208	+	0.793011i	$0.708512\pi$
$270$		0			0
$271$	1.53590	−	2.66025i	0.0932992	−	0.161599i	−0.815598	−	0.578619i	$-0.803592\pi$
$271$	1.53590	−	2.66025i	0.0932992	−	0.161599i	0.908897	+	0.417020i	$0.136925\pi$
$272$		0			0
$273$	−3.92820	+	4.53590i	−0.237746	+	0.274525i
$274$		0			0
$275$	0.366025	−	0.633975i	0.0220722	−	0.0382301i
$276$		0			0
$277$	7.33013	+	12.6962i	0.440425	+	0.762838i	0.997721	−	0.0674759i	$-0.0214946\pi$
$277$	7.33013	+	12.6962i	0.440425	+	0.762838i	−0.557296	+	0.830314i	$0.688161\pi$
$278$		0			0
$279$	0.464102			0.0277850
$280$		0			0
$281$	13.8564			0.826604			0.413302	−	0.910594i	$-0.364375\pi$
$281$	13.8564			0.826604			0.413302	+	0.910594i	$0.364375\pi$
$282$		0			0
$283$	−12.0622	−	20.8923i	−0.717022	−	1.24192i	−0.962174	−	0.272434i	$-0.912171\pi$
$283$	−12.0622	−	20.8923i	−0.717022	−	1.24192i	0.245152	−	0.969485i	$-0.421162\pi$
$284$		0			0
$285$	2.23205	−	3.86603i	0.132215	−	0.229004i
$286$		0			0
$287$	0.633975	+	1.83013i	0.0374223	+	0.108029i
$288$		0			0
$289$	3.16025	−	5.47372i	0.185897	−	0.321984i
$290$		0			0
$291$	−7.46410	−	12.9282i	−0.437553	−	0.757865i
$292$		0			0
$293$	18.9282			1.10580			0.552899	−	0.833248i	$-0.313522\pi$
$293$	18.9282			1.10580			0.552899	+	0.833248i	$0.313522\pi$
$294$		0			0
$295$	0.196152			0.0114204
$296$		0			0
$297$	0.366025	+	0.633975i	0.0212389	+	0.0367869i
$298$		0			0
$299$	−5.36603	+	9.29423i	−0.310325	+	0.537499i
$300$		0			0
$301$	2.76795	+	7.99038i	0.159542	+	0.460558i
$302$		0			0
$303$	3.63397	−	6.29423i	0.208766	−	0.361594i
$304$		0			0
$305$	−2.00000	−	3.46410i	−0.114520	−	0.198354i
$306$		0			0
$307$	32.1244			1.83343			0.916717	−	0.399537i	$-0.130829\pi$
$307$	32.1244			1.83343			0.916717	+	0.399537i	$0.130829\pi$
$308$		0			0
$309$	9.19615			0.523151
$310$		0			0
$311$	4.56218	+	7.90192i	0.258697	+	0.448077i	0.965893	−	0.258941i	$-0.0833734\pi$
$311$	4.56218	+	7.90192i	0.258697	+	0.448077i	−0.707196	+	0.707018i	$0.750040\pi$
$312$		0			0
$313$	6.33013	−	10.9641i	0.357800	−	0.619728i	−0.629793	−	0.776763i	$-0.716860\pi$
$313$	6.33013	−	10.9641i	0.357800	−	0.619728i	0.987593	+	0.157035i	$0.0501936\pi$
$314$		0			0
$315$	−1.73205	+	2.00000i	−0.0975900	+	0.112687i
$316$		0			0
$317$	14.2224	−	24.6340i	0.798811	−	1.38358i	−0.121579	−	0.992582i	$-0.538796\pi$
$317$	14.2224	−	24.6340i	0.798811	−	1.38358i	0.920391	−	0.391000i	$-0.127871\pi$
$318$		0			0
$319$	−1.53590	−	2.66025i	−0.0859938	−	0.148946i
$320$		0			0
$321$	−2.19615			−0.122577
$322$		0			0
$323$	−14.5885			−0.811723
$324$		0			0
$325$	−1.13397	−	1.96410i	−0.0629016	−	0.108949i
$326$		0			0
$327$	−5.50000	+	9.52628i	−0.304151	+	0.526804i
$328$		0			0
$329$	−5.19615	−	1.00000i	−0.286473	−	0.0551318i
$330$		0			0
$331$	4.03590	−	6.99038i	0.221833	−	0.384226i	−0.733532	−	0.679655i	$-0.762129\pi$
$331$	4.03590	−	6.99038i	0.221833	−	0.384226i	0.955365	+	0.295429i	$0.0954627\pi$
$332$		0			0
$333$	1.59808	+	2.76795i	0.0875740	+	0.151683i
$334$		0			0
$335$	14.6603			0.800975
$336$		0			0
$337$	17.9808			0.979475			0.489737	−	0.871870i	$-0.337093\pi$
$337$	17.9808			0.979475			0.489737	+	0.871870i	$0.337093\pi$
$338$		0			0
$339$	−4.46410	−	7.73205i	−0.242457	−	0.419947i
$340$		0			0
$341$	0.169873	−	0.294229i	0.00919914	−	0.0159334i
$342$		0			0
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$		0			0
$345$	−2.36603	+	4.09808i	−0.127383	+	0.220633i
$346$		0			0
$347$	−10.5359	−	18.2487i	−0.565597	−	0.979642i	−0.996994	−	0.0774801i	$-0.975313\pi$
$347$	−10.5359	−	18.2487i	−0.565597	−	0.979642i	0.431397	−	0.902162i	$-0.358021\pi$
$348$		0			0
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$		0			0
$351$	2.26795			0.121054
$352$		0			0
$353$	1.56218	+	2.70577i	0.0831463	+	0.144014i	0.904600	−	0.426262i	$-0.140170\pi$
$353$	1.56218	+	2.70577i	0.0831463	+	0.144014i	−0.821453	+	0.570276i	$0.806836\pi$
$354$		0			0
$355$	3.09808	−	5.36603i	0.164429	−	0.284799i
$356$		0			0
$357$	8.49038	+	1.63397i	0.449359	+	0.0864791i
$358$		0			0
$359$	−0.633975	+	1.09808i	−0.0334599	+	0.0579542i	−0.882270	−	0.470743i	$-0.843986\pi$
$359$	−0.633975	+	1.09808i	−0.0334599	+	0.0579542i	0.848811	+	0.528697i	$0.177319\pi$
$360$		0			0
$361$	−0.464102	−	0.803848i	−0.0244264	−	0.0423078i
$362$		0			0
$363$	−10.4641			−0.549223
$364$		0			0
$365$	12.6603			0.662668
$366$		0			0
$367$	5.59808	+	9.69615i	0.292217	+	0.506135i	0.974334	−	0.225108i	$-0.0722736\pi$
$367$	5.59808	+	9.69615i	0.292217	+	0.506135i	−0.682117	+	0.731244i	$0.738940\pi$
$368$		0			0
$369$	0.366025	−	0.633975i	0.0190545	−	0.0330034i
$370$		0			0
$371$	−21.4641	+	24.7846i	−1.11436	+	1.28675i
$372$		0			0
$373$	−13.2583	+	22.9641i	−0.686490	+	1.18904i	0.286476	+	0.958088i	$0.407516\pi$
$373$	−13.2583	+	22.9641i	−0.686490	+	1.18904i	−0.972966	+	0.230949i	$0.925817\pi$
$374$		0			0
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	−9.51666			−0.490133
$378$		0			0
$379$	−6.32051			−0.324663			−0.162331	−	0.986736i	$-0.551901\pi$
$379$	−6.32051			−0.324663			−0.162331	+	0.986736i	$0.551901\pi$
$380$		0			0
$381$	2.40192	+	4.16025i	0.123054	+	0.213136i
$382$		0			0
$383$	−11.6603	+	20.1962i	−0.595811	+	1.03198i	0.397621	+	0.917550i	$0.369836\pi$
$383$	−11.6603	+	20.1962i	−0.595811	+	1.03198i	−0.993432	+	0.114425i	$0.963497\pi$
$384$		0			0
$385$	0.633975	+	1.83013i	0.0323103	+	0.0932719i
$386$		0			0
$387$	1.59808	−	2.76795i	0.0812348	−	0.140703i
$388$		0			0
$389$	−2.70577	−	4.68653i	−0.137188	−	0.237617i	0.789243	−	0.614081i	$-0.210473\pi$
$389$	−2.70577	−	4.68653i	−0.137188	−	0.237617i	−0.926431	+	0.376464i	$0.877140\pi$
$390$		0			0
$391$	15.4641			0.782053
$392$		0			0
$393$	−15.4641			−0.780061
$394$		0			0
$395$	−3.69615	−	6.40192i	−0.185974	−	0.322116i
$396$		0			0
$397$	15.5981	−	27.0167i	0.782845	−	1.35593i	−0.147433	−	0.989072i	$-0.547101\pi$
$397$	15.5981	−	27.0167i	0.782845	−	1.35593i	0.930278	−	0.366855i	$-0.119566\pi$
$398$		0			0
$399$	3.86603	+	11.1603i	0.193543	+	0.558712i
$400$		0			0
$401$	8.19615	−	14.1962i	0.409296	−	0.708922i	−0.585515	−	0.810662i	$-0.699108\pi$
$401$	8.19615	−	14.1962i	0.409296	−	0.708922i	0.994811	+	0.101740i	$0.0324409\pi$
$402$		0			0
$403$	−0.526279	−	0.911543i	−0.0262158	−	0.0454072i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	2.33975			0.115977
$408$		0			0
$409$	−1.57180	−	2.72243i	−0.0777203	−	0.134616i	0.824546	−	0.565795i	$-0.191431\pi$
$409$	−1.57180	−	2.72243i	−0.0777203	−	0.134616i	−0.902266	+	0.431180i	$0.858097\pi$
$410$		0			0
$411$	−1.09808	+	1.90192i	−0.0541641	+	0.0938150i
$412$		0			0
$413$	−0.339746	+	0.392305i	−0.0167178	+	0.0193041i
$414$		0			0
$415$	7.56218	−	13.0981i	0.371213	−	0.642959i
$416$		0			0
$417$	2.96410	+	5.13397i	0.145153	+	0.251412i
$418$		0			0
$419$	35.4641			1.73253			0.866267	−	0.499581i	$-0.166513\pi$
$419$	35.4641			1.73253			0.866267	+	0.499581i	$0.166513\pi$
$420$		0			0
$421$	0.0717968			0.00349916			0.00174958	−	0.999998i	$-0.499443\pi$
$421$	0.0717968			0.00349916			0.00174958	+	0.999998i	$0.499443\pi$
$422$		0			0
$423$	1.00000	+	1.73205i	0.0486217	+	0.0842152i
$424$		0			0
$425$	−1.63397	+	2.83013i	−0.0792594	+	0.137281i
$426$		0			0
$427$	10.3923	+	2.00000i	0.502919	+	0.0967868i
$428$		0			0
$429$	0.830127	−	1.43782i	0.0400789	−	0.0694187i
$430$		0			0
$431$	8.66025	+	15.0000i	0.417150	+	0.722525i	0.995651	−	0.0931566i	$-0.0296957\pi$
$431$	8.66025	+	15.0000i	0.417150	+	0.722525i	−0.578502	+	0.815681i	$0.696362\pi$
$432$		0			0
$433$	15.1962			0.730280			0.365140	−	0.930953i	$-0.381021\pi$
$433$	15.1962			0.730280			0.365140	+	0.930953i	$0.381021\pi$
$434$		0			0
$435$	−4.19615			−0.201190
$436$		0			0
$437$	10.5622	+	18.2942i	0.505257	+	0.875132i
$438$		0			0
$439$	0.267949	−	0.464102i	0.0127885	−	0.0221504i	−0.859560	−	0.511034i	$-0.829263\pi$
$439$	0.267949	−	0.464102i	0.0127885	−	0.0221504i	0.872349	+	0.488884i	$0.162596\pi$
$440$		0			0
$441$	−1.00000	−	6.92820i	−0.0476190	−	0.329914i
$442$		0			0
$443$	4.73205	−	8.19615i	0.224827	−	0.389411i	−0.731441	−	0.681905i	$-0.761152\pi$
$443$	4.73205	−	8.19615i	0.224827	−	0.389411i	0.956267	+	0.292494i	$0.0944851\pi$
$444$		0			0
$445$	−7.56218	−	13.0981i	−0.358482	−	0.620908i
$446$		0			0
$447$	5.85641			0.276999
$448$		0			0
$449$	−35.8564			−1.69217			−0.846084	−	0.533049i	$-0.821046\pi$
$449$	−35.8564			−1.69217			−0.846084	+	0.533049i	$0.821046\pi$
$450$		0			0
$451$	−0.267949	−	0.464102i	−0.0126172	−	0.0218537i
$452$		0			0
$453$	−4.46410	+	7.73205i	−0.209742	+	0.363283i
$454$		0			0
$455$	5.89230	+	1.13397i	0.276236	+	0.0531615i
$456$		0			0
$457$	8.33013	−	14.4282i	0.389667	−	0.674923i	−0.602738	−	0.797939i	$-0.705923\pi$
$457$	8.33013	−	14.4282i	0.389667	−	0.674923i	0.992405	+	0.123016i	$0.0392568\pi$
$458$		0			0
$459$	−1.63397	−	2.83013i	−0.0762674	−	0.132099i
$460$		0			0
$461$	16.9808			0.790873			0.395436	−	0.918493i	$-0.370593\pi$
$461$	16.9808			0.790873			0.395436	+	0.918493i	$0.370593\pi$
$462$		0			0
$463$	−25.7321			−1.19587			−0.597935	−	0.801545i	$-0.704012\pi$
$463$	−25.7321			−1.19587			−0.597935	+	0.801545i	$0.704012\pi$
$464$		0			0
$465$	−0.232051	−	0.401924i	−0.0107611	−	0.0186388i
$466$		0			0
$467$	−0.0717968	+	0.124356i	−0.00332236	+	0.00575449i	−0.867682	−	0.497120i	$-0.834391\pi$
$467$	−0.0717968	+	0.124356i	−0.00332236	+	0.00575449i	0.864359	+	0.502874i	$0.167724\pi$
$468$		0			0
$469$	−25.3923	+	29.3205i	−1.17251	+	1.35390i
$470$		0			0
$471$	−3.19615	+	5.53590i	−0.147271	+	0.255081i
$472$		0			0
$473$	−1.16987	−	2.02628i	−0.0537908	−	0.0931684i
$474$		0			0
$475$	−4.46410			−0.204827
$476$		0			0
$477$	12.3923			0.567405
$478$		0			0
$479$	4.39230	+	7.60770i	0.200690	+	0.347604i	0.948751	−	0.316025i	$-0.102348\pi$
$479$	4.39230	+	7.60770i	0.200690	+	0.347604i	−0.748061	+	0.663630i	$0.769015\pi$
$480$		0			0
$481$	3.62436	−	6.27757i	0.165256	−	0.286232i
$482$		0			0
$483$	−4.09808	−	11.8301i	−0.186469	−	0.538289i
$484$		0			0
$485$	−7.46410	+	12.9282i	−0.338927	+	0.587039i
$486$		0			0
$487$	−0.205771	−	0.356406i	−0.00932439	−	0.0161503i	0.861326	−	0.508053i	$-0.169635\pi$
$487$	−0.205771	−	0.356406i	−0.00932439	−	0.0161503i	−0.870650	+	0.491903i	$0.836301\pi$
$488$		0			0
$489$	−21.8564			−0.988381
$490$		0			0
$491$	38.2487			1.72614			0.863070	−	0.505084i	$-0.168539\pi$
$491$	38.2487			1.72614			0.863070	+	0.505084i	$0.168539\pi$
$492$		0			0
$493$	6.85641	+	11.8756i	0.308797	+	0.534852i
$494$		0			0
$495$	0.366025	−	0.633975i	0.0164516	−	0.0284950i
$496$		0			0
$497$	5.36603	+	15.4904i	0.240699	+	0.694839i
$498$		0			0
$499$	−6.76795	+	11.7224i	−0.302975	+	0.524768i	−0.976808	−	0.214115i	$-0.931313\pi$
$499$	−6.76795	+	11.7224i	−0.302975	+	0.524768i	0.673833	+	0.738883i	$0.264647\pi$
$500$		0			0
$501$	−8.83013	−	15.2942i	−0.394501	−	0.683296i
$502$		0			0
$503$	−14.3923			−0.641721			−0.320861	−	0.947126i	$-0.603972\pi$
$503$	−14.3923			−0.641721			−0.320861	+	0.947126i	$0.603972\pi$
$504$		0			0
$505$	−7.26795			−0.323419
$506$		0			0
$507$	3.92820	+	6.80385i	0.174458	+	0.302169i
$508$		0			0
$509$	−2.26795	+	3.92820i	−0.100525	+	0.174115i	−0.911901	−	0.410410i	$-0.865386\pi$
$509$	−2.26795	+	3.92820i	−0.100525	+	0.174115i	0.811376	+	0.584525i	$0.198719\pi$
$510$		0			0
$511$	−21.9282	+	25.3205i	−0.970047	+	1.12011i
$512$		0			0
$513$	2.23205	−	3.86603i	0.0985475	−	0.170689i
$514$		0			0
$515$	−4.59808	−	7.96410i	−0.202615	−	0.350940i
$516$		0			0
$517$	1.46410			0.0643911
$518$		0			0
$519$	14.5359			0.638055
$520$		0			0
$521$	2.73205	+	4.73205i	0.119693	+	0.207315i	0.919646	−	0.392748i	$-0.128476\pi$
$521$	2.73205	+	4.73205i	0.119693	+	0.207315i	−0.799953	+	0.600063i	$0.795142\pi$
$522$		0			0
$523$	−13.8660	+	24.0167i	−0.606319	+	1.05018i	0.385523	+	0.922698i	$0.374021\pi$
$523$	−13.8660	+	24.0167i	−0.606319	+	1.05018i	−0.991842	+	0.127477i	$0.959312\pi$
$524$		0			0
$525$	2.59808	+	0.500000i	0.113389	+	0.0218218i
$526$		0			0
$527$	−0.758330	+	1.31347i	−0.0330334	+	0.0572155i
$528$		0			0
$529$	0.303848	+	0.526279i	0.0132108	+	0.0228817i
$530$		0			0
$531$	0.196152			0.00851229
$532$		0			0
$533$	−1.66025			−0.0719136
$534$		0			0
$535$	1.09808	+	1.90192i	0.0474740	+	0.0822273i
$536$		0			0
$537$	−5.00000	+	8.66025i	−0.215766	+	0.373718i
$538$		0			0
$539$	−4.75833	−	1.90192i	−0.204956	−	0.0819217i
$540$		0			0
$541$	−2.89230	+	5.00962i	−0.124350	+	0.215380i	−0.921479	−	0.388429i	$-0.873018\pi$
$541$	−2.89230	+	5.00962i	−0.124350	+	0.215380i	0.797129	+	0.603809i	$0.206351\pi$
$542$		0			0
$543$	12.1603	+	21.0622i	0.521846	+	0.903865i
$544$		0			0
$545$	11.0000			0.471188
$546$		0			0
$547$	26.2487			1.12231			0.561157	−	0.827709i	$-0.310356\pi$
$547$	26.2487			1.12231			0.561157	+	0.827709i	$0.310356\pi$
$548$		0			0
$549$	−2.00000	−	3.46410i	−0.0853579	−	0.147844i
$550$		0			0
$551$	−9.36603	+	16.2224i	−0.399006	+	0.691099i
$552$		0			0
$553$	19.2058	+	3.69615i	0.816712	+	0.157176i
$554$		0			0
$555$	1.59808	−	2.76795i	0.0678346	−	0.117493i
$556$		0			0
$557$	−7.39230	−	12.8038i	−0.313222	−	0.542516i	0.665836	−	0.746098i	$-0.268075\pi$
$557$	−7.39230	−	12.8038i	−0.313222	−	0.542516i	−0.979058	+	0.203582i	$0.934742\pi$
$558$		0			0
$559$	−7.24871			−0.306588
$560$		0			0
$561$	−2.39230			−0.101003
$562$		0			0
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	0.611656	−	0.791123i	$-0.290503\pi$
$563$	−9.00000	−	15.5885i	−0.379305	−	0.656975i	−0.990961	+	0.134148i	$0.957170\pi$
$564$		0			0
$565$	−4.46410	+	7.73205i	−0.187806	+	0.325290i
$566$		0			0
$567$	−1.73205	+	2.00000i	−0.0727393	+	0.0839921i
$568$		0			0
$569$	−16.2224	+	28.0981i	−0.680080	+	1.17793i	0.294876	+	0.955535i	$0.404722\pi$
$569$	−16.2224	+	28.0981i	−0.680080	+	1.17793i	−0.974956	+	0.222397i	$0.928612\pi$
$570$		0			0
$571$	9.30385	+	16.1147i	0.389354	+	0.674381i	0.992363	−	0.123354i	$-0.0393650\pi$
$571$	9.30385	+	16.1147i	0.389354	+	0.674381i	−0.603009	+	0.797734i	$0.706032\pi$
$572$		0			0
$573$	8.92820			0.372981
$574$		0			0
$575$	4.73205			0.197340
$576$		0			0
$577$	−14.3301	−	24.8205i	−0.596571	−	1.03329i	−0.993323	−	0.115365i	$-0.963196\pi$
$577$	−14.3301	−	24.8205i	−0.596571	−	1.03329i	0.396752	−	0.917926i	$-0.370137\pi$
$578$		0			0
$579$	−0.598076	+	1.03590i	−0.0248552	+	0.0430505i
$580$		0			0
$581$	13.0981	+	37.8109i	0.543400	+	1.56866i
$582$		0			0
$583$	4.53590	−	7.85641i	0.187858	−	0.325379i
$584$		0			0
$585$	−1.13397	−	1.96410i	−0.0468841	−	0.0812056i
$586$		0			0
$587$	−40.7321			−1.68119			−0.840596	−	0.541663i	$-0.817795\pi$
$587$	−40.7321			−1.68119			−0.840596	+	0.541663i	$0.817795\pi$
$588$		0			0
$589$	−2.07180			−0.0853669
$590$		0			0
$591$	0.169873	+	0.294229i	0.00698764	+	0.0121029i
$592$		0			0
$593$	−13.9545	+	24.1699i	−0.573042	+	0.992538i	0.423209	+	0.906032i	$0.360903\pi$
$593$	−13.9545	+	24.1699i	−0.573042	+	0.992538i	−0.996251	+	0.0865058i	$0.972430\pi$
$594$		0			0
$595$	−2.83013	−	8.16987i	−0.116024	−	0.334932i
$596$		0			0
$597$	11.0000	−	19.0526i	0.450200	−	0.779769i
$598$		0			0
$599$	−19.1244	−	33.1244i	−0.781400	−	1.35342i	−0.931126	−	0.364697i	$-0.881173\pi$
$599$	−19.1244	−	33.1244i	−0.781400	−	1.35342i	0.149726	−	0.988727i	$-0.452161\pi$
$600$		0			0
$601$	−0.0717968			−0.00292865			−0.00146433	−	0.999999i	$-0.500466\pi$
$601$	−0.0717968			−0.00292865			−0.00146433	+	0.999999i	$0.500466\pi$
$602$		0			0
$603$	14.6603			0.597012
$604$		0			0
$605$	5.23205	+	9.06218i	0.212713	+	0.368430i
$606$		0			0
$607$	1.59808	−	2.76795i	0.0648639	−	0.112348i	−0.831770	−	0.555121i	$-0.812672\pi$
$607$	1.59808	−	2.76795i	0.0648639	−	0.112348i	0.896634	+	0.442773i	$0.146005\pi$
$608$		0			0
$609$	7.26795	−	8.39230i	0.294512	−	0.340073i
$610$		0			0
$611$	2.26795	−	3.92820i	0.0917514	−	0.158918i
$612$		0			0
$613$	13.4641	+	23.3205i	0.543810	+	0.941906i	0.998681	+	0.0513490i	$0.0163521\pi$
$613$	13.4641	+	23.3205i	0.543810	+	0.941906i	−0.454871	+	0.890557i	$0.650315\pi$
$614$		0			0
$615$	−0.732051			−0.0295191
$616$		0			0
$617$	−36.2487			−1.45932			−0.729659	−	0.683811i	$-0.760321\pi$
$617$	−36.2487			−1.45932			−0.729659	+	0.683811i	$0.760321\pi$
$618$		0			0
$619$	−15.0359	−	26.0429i	−0.604344	−	1.04675i	−0.992155	−	0.125015i	$-0.960102\pi$
$619$	−15.0359	−	26.0429i	−0.604344	−	1.04675i	0.387811	−	0.921739i	$-0.373231\pi$
$620$		0			0
$621$	−2.36603	+	4.09808i	−0.0949453	+	0.164450i
$622$		0			0
$623$	39.2942	+	7.56218i	1.57429	+	0.302972i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−1.63397	−	2.83013i	−0.0652547	−	0.113024i
$628$		0			0
$629$	−10.4449			−0.416464
$630$		0			0
$631$	−48.7846			−1.94208			−0.971042	−	0.238908i	$-0.923211\pi$
$631$	−48.7846			−1.94208			−0.971042	+	0.238908i	$0.923211\pi$
$632$		0			0
$633$	3.53590	+	6.12436i	0.140539	+	0.243421i
$634$		0			0
$635$	2.40192	−	4.16025i	0.0953174	−	0.165095i
$636$		0			0
$637$	−12.4737	+	9.82051i	−0.494227	+	0.389103i
$638$		0			0
$639$	3.09808	−	5.36603i	0.122558	−	0.212277i
$640$		0			0
$641$	−1.90192	−	3.29423i	−0.0751215	−	0.130114i	0.826018	−	0.563644i	$-0.190601\pi$
$641$	−1.90192	−	3.29423i	−0.0751215	−	0.130114i	−0.901139	+	0.433530i	$0.857268\pi$
$642$		0			0
$643$	−4.51666			−0.178120			−0.0890599	−	0.996026i	$-0.528386\pi$
$643$	−4.51666			−0.178120			−0.0890599	+	0.996026i	$0.528386\pi$
$644$		0			0
$645$	−3.19615			−0.125848
$646$		0			0
$647$	−13.9545	−	24.1699i	−0.548607	−	0.950216i	−0.998370	−	0.0570678i	$-0.981825\pi$
$647$	−13.9545	−	24.1699i	−0.548607	−	0.950216i	0.449763	−	0.893148i	$-0.351508\pi$
$648$		0			0
$649$	0.0717968	−	0.124356i	0.00281827	−	0.00488139i
$650$		0			0
$651$	1.20577	+	0.232051i	0.0472579	+	0.00909479i
$652$		0			0
$653$	22.2942	−	38.6147i	0.872441	−	1.51111i	0.0129762	−	0.999916i	$-0.495869\pi$
$653$	22.2942	−	38.6147i	0.872441	−	1.51111i	0.859464	−	0.511196i	$-0.170797\pi$
$654$		0			0
$655$	7.73205	+	13.3923i	0.302116	+	0.523281i
$656$		0			0
$657$	12.6603			0.493924
$658$		0			0
$659$	−2.92820			−0.114067			−0.0570333	−	0.998372i	$-0.518164\pi$
$659$	−2.92820			−0.114067			−0.0570333	+	0.998372i	$0.518164\pi$
$660$		0			0
$661$	−5.23205	−	9.06218i	−0.203503	−	0.352478i	0.746152	−	0.665776i	$-0.231899\pi$
$661$	−5.23205	−	9.06218i	−0.203503	−	0.352478i	−0.949655	+	0.313298i	$0.898566\pi$
$662$		0			0
$663$	−3.70577	+	6.41858i	−0.143920	+	0.249277i
$664$		0			0
$665$	7.73205	−	8.92820i	0.299836	−	0.346221i
$666$		0			0
$667$	9.92820	−	17.1962i	0.384422	−	0.665838i
$668$		0			0
$669$	−10.1962	−	17.6603i	−0.394206	−	0.682785i
$670$		0			0
$671$	−2.92820			−0.113042
$672$		0			0
$673$	−27.3397			−1.05387			−0.526935	−	0.849906i	$-0.676659\pi$
$673$	−27.3397			−1.05387			−0.526935	+	0.849906i	$0.676659\pi$
$674$		0			0
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$		0			0
$677$	16.5622	−	28.6865i	0.636536	−	1.10251i	−0.349651	−	0.936880i	$-0.613700\pi$
$677$	16.5622	−	28.6865i	0.636536	−	1.10251i	0.986187	−	0.165633i	$-0.0529668\pi$
$678$		0			0
$679$	−12.9282	−	37.3205i	−0.496139	−	1.43223i
$680$		0			0
$681$	−0.830127	+	1.43782i	−0.0318105	+	0.0550975i
$682$		0			0
$683$	−14.0263	−	24.2942i	−0.536701	−	0.929593i	−0.999079	−	0.0429101i	$-0.986337\pi$
$683$	−14.0263	−	24.2942i	−0.536701	−	0.929593i	0.462378	−	0.886683i	$-0.346996\pi$
$684$		0			0
$685$	2.19615			0.0839107
$686$		0			0
$687$	−3.00000			−0.114457
$688$		0			0
$689$	−14.0526	−	24.3397i	−0.535360	−	0.927270i
$690$		0			0
$691$	4.42820	−	7.66987i	0.168457	−	0.291776i	−0.769421	−	0.638742i	$-0.779455\pi$
$691$	4.42820	−	7.66987i	0.168457	−	0.291776i	0.937877	+	0.346967i	$0.112788\pi$
$692$		0			0
$693$	0.633975	+	1.83013i	0.0240827	+	0.0695208i
$694$		0			0
$695$	2.96410	−	5.13397i	0.112435	−	0.194743i
$696$		0			0
$697$	1.19615	+	2.07180i	0.0453075	+	0.0784749i
$698$		0			0
$699$	17.3205			0.655122
$700$		0			0
$701$	−8.58846			−0.324382			−0.162191	−	0.986759i	$-0.551856\pi$
$701$	−8.58846			−0.324382			−0.162191	+	0.986759i	$0.551856\pi$
$702$		0			0
$703$	−7.13397	−	12.3564i	−0.269063	−	0.466031i
$704$		0			0
$705$	1.00000	−	1.73205i	0.0376622	−	0.0652328i
$706$		0			0
$707$	12.5885	−	14.5359i	0.473438	−	0.546679i
$708$		0			0
$709$	0.535898	−	0.928203i	0.0201261	−	0.0348594i	−0.855787	−	0.517328i	$-0.826927\pi$
$709$	0.535898	−	0.928203i	0.0201261	−	0.0348594i	0.875913	+	0.482469i	$0.160260\pi$
$710$		0			0
$711$	−3.69615	−	6.40192i	−0.138617	−	0.240091i
$712$		0			0
$713$	2.19615			0.0822466
$714$		0			0
$715$	−1.66025			−0.0620900
$716$		0			0
$717$	3.53590	+	6.12436i	0.132051	+	0.228718i
$718$		0			0
$719$	−10.2679	+	17.7846i	−0.382930	+	0.663254i	−0.991480	−	0.130262i	$-0.958418\pi$
$719$	−10.2679	+	17.7846i	−0.382930	+	0.663254i	0.608550	+	0.793516i	$0.291752\pi$
$720$		0			0
$721$	23.8923	+	4.59808i	0.889796	+	0.171241i
$722$		0			0
$723$	−6.73205	+	11.6603i	−0.250368	+	0.433650i
$724$		0			0
$725$	2.09808	+	3.63397i	0.0779206	+	0.134962i
$726$		0			0
$727$	13.3397			0.494744			0.247372	−	0.968921i	$-0.420433\pi$
$727$	13.3397			0.494744			0.247372	+	0.968921i	$0.420433\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	5.22243	+	9.04552i	0.193159	+	0.334561i
$732$		0			0
$733$	0.669873	−	1.16025i	0.0247423	−	0.0428550i	−0.853389	−	0.521274i	$-0.825457\pi$
$733$	0.669873	−	1.16025i	0.0247423	−	0.0428550i	0.878131	+	0.478419i	$0.158790\pi$
$734$		0			0
$735$	−5.50000	+	4.33013i	−0.202871	+	0.159719i
$736$		0			0
$737$	5.36603	−	9.29423i	0.197660	−	0.342357i
$738$		0			0
$739$	13.8923	+	24.0622i	0.511037	+	0.885142i	0.999918	+	0.0127913i	$0.00407171\pi$
$739$	13.8923	+	24.0622i	0.511037	+	0.885142i	−0.488881	+	0.872350i	$0.662595\pi$
$740$		0			0
$741$	−10.1244			−0.371927
$742$		0			0
$743$	15.9090			0.583643			0.291822	−	0.956473i	$-0.405739\pi$
$743$	15.9090			0.583643			0.291822	+	0.956473i	$0.405739\pi$
$744$		0			0
$745$	−2.92820	−	5.07180i	−0.107281	−	0.185816i
$746$		0			0
$747$	7.56218	−	13.0981i	0.276686	−	0.479234i
$748$		0			0
$749$	−5.70577	−	1.09808i	−0.208484	−	0.0401228i
$750$		0			0
$751$	9.03590	−	15.6506i	0.329725	−	0.571100i	−0.652732	−	0.757588i	$-0.726377\pi$
$751$	9.03590	−	15.6506i	0.329725	−	0.571100i	0.982457	+	0.186489i	$0.0597108\pi$
$752$		0			0
$753$	−12.2942	−	21.2942i	−0.448027	−	0.776005i
$754$		0			0
$755$	8.92820			0.324931
$756$		0			0
$757$	−27.8564			−1.01246			−0.506229	−	0.862399i	$-0.668961\pi$
$757$	−27.8564			−1.01246			−0.506229	+	0.862399i	$0.668961\pi$
$758$		0			0
$759$	1.73205	+	3.00000i	0.0628695	+	0.108893i
$760$		0			0
$761$	−23.3660	+	40.4711i	−0.847018	+	1.46708i	0.0368396	+	0.999321i	$0.488271\pi$
$761$	−23.3660	+	40.4711i	−0.847018	+	1.46708i	−0.883857	+	0.467757i	$0.845062\pi$
$762$		0			0
$763$	−19.0526	+	22.0000i	−0.689749	+	0.796453i
$764$		0			0
$765$	−1.63397	+	2.83013i	−0.0590765	+	0.102323i
$766$		0			0
$767$	−0.222432	−	0.385263i	−0.00803155	−	0.0139111i
$768$		0			0
$769$	52.3205			1.88673			0.943363	−	0.331763i	$-0.107643\pi$
$769$	52.3205			1.88673			0.943363	+	0.331763i	$0.107643\pi$
$770$		0			0
$771$	−5.66025			−0.203849
$772$		0			0
$773$	−21.7583	−	37.6865i	−0.782593	−	1.35549i	−0.930427	−	0.366478i	$-0.880563\pi$
$773$	−21.7583	−	37.6865i	−0.782593	−	1.35549i	0.147834	−	0.989012i	$-0.452770\pi$
$774$		0			0
$775$	−0.232051	+	0.401924i	−0.00833551	+	0.0144375i
$776$		0			0
$777$	2.76795	+	7.99038i	0.0992996	+	0.286653i
$778$		0			0
$779$	−1.63397	+	2.83013i	−0.0585432	+	0.101400i
$780$		0			0
$781$	−2.26795	−	3.92820i	−0.0811536	−	0.140562i
$782$		0			0
$783$	−4.19615			−0.149958
$784$		0			0
$785$	6.39230			0.228151
$786$		0			0
$787$	6.73205	+	11.6603i	0.239972	+	0.415643i	0.960706	−	0.277568i	$-0.0895285\pi$
$787$	6.73205	+	11.6603i	0.239972	+	0.415643i	−0.720734	+	0.693212i	$0.756195\pi$
$788$		0			0
$789$	4.19615	−	7.26795i	0.149387	−	0.258746i
$790$		0			0
$791$	−7.73205	−	22.3205i	−0.274920	−	0.793626i
$792$		0			0
$793$	−4.53590	+	7.85641i	−0.161074	+	0.278989i
$794$		0			0
$795$	−6.19615	−	10.7321i	−0.219755	−	0.380627i
$796$		0			0
$797$	−3.94744			−0.139826			−0.0699128	−	0.997553i	$-0.522272\pi$
$797$	−3.94744			−0.139826			−0.0699128	+	0.997553i	$0.522272\pi$
$798$		0			0
$799$	−6.53590			−0.231223
$800$		0			0
$801$	−7.56218	−	13.0981i	−0.267196	−	0.462798i
$802$		0			0
$803$	4.63397	−	8.02628i	0.163529	−	0.283241i
$804$		0			0
$805$	−8.19615	+	9.46410i	−0.288876	+	0.333566i
$806$		0			0
$807$	6.26795	−	10.8564i	0.220642	−	0.382164i
$808$		0			0
$809$	−12.8564	−	22.2679i	−0.452007	−	0.782899i	0.546503	−	0.837457i	$-0.315959\pi$
$809$	−12.8564	−	22.2679i	−0.452007	−	0.782899i	−0.998511	+	0.0545574i	$0.982625\pi$
$810$		0			0
$811$	3.46410			0.121641			0.0608205	−	0.998149i	$-0.480628\pi$
$811$	3.46410			0.121641			0.0608205	+	0.998149i	$0.480628\pi$
$812$		0			0
$813$	−3.07180			−0.107733
$814$		0			0
$815$	10.9282	+	18.9282i	0.382798	+	0.663026i
$816$		0			0
$817$	−7.13397	+	12.3564i	−0.249586	+	0.432296i
$818$		0			0
$819$	5.89230	+	1.13397i	0.205894	+	0.0396243i
$820$		0			0
$821$	12.7583	−	22.0981i	0.445269	−	0.771228i	−0.552802	−	0.833313i	$-0.686441\pi$
$821$	12.7583	−	22.0981i	0.445269	−	0.771228i	0.998071	+	0.0620844i	$0.0197748\pi$
$822$		0			0
$823$	19.5885	+	33.9282i	0.682811	+	1.18266i	0.974119	+	0.226034i	$0.0725760\pi$
$823$	19.5885	+	33.9282i	0.682811	+	1.18266i	−0.291309	+	0.956629i	$0.594091\pi$
$824$		0			0
$825$	−0.732051			−0.0254867
$826$		0			0
$827$	3.75129			0.130445			0.0652225	−	0.997871i	$-0.479224\pi$
$827$	3.75129			0.130445			0.0652225	+	0.997871i	$0.479224\pi$
$828$		0			0
$829$	2.30385	+	3.99038i	0.0800159	+	0.138592i	0.903257	−	0.429101i	$-0.141170\pi$
$829$	2.30385	+	3.99038i	0.0800159	+	0.138592i	−0.823241	+	0.567693i	$0.807836\pi$
$830$		0			0
$831$	7.33013	−	12.6962i	0.254279	−	0.440425i
$832$		0			0
$833$	21.2417	+	8.49038i	0.735980	+	0.294174i
$834$		0			0
$835$	−8.83013	+	15.2942i	−0.305579	+	0.529279i
$836$		0			0
$837$	−0.232051	−	0.401924i	−0.00802085	−	0.0138925i
$838$		0			0
$839$	−18.4449			−0.636787			−0.318394	−	0.947959i	$-0.603143\pi$
$839$	−18.4449			−0.636787			−0.318394	+	0.947959i	$0.603143\pi$
$840$		0			0
$841$	−11.3923			−0.392838
$842$		0			0
$843$	−6.92820	−	12.0000i	−0.238620	−	0.413302i
$844$		0			0
$845$	3.92820	−	6.80385i	0.135134	−	0.234059i
$846$		0			0
$847$	−27.1865	−	5.23205i	−0.934140	−	0.179775i
$848$		0			0
$849$	−12.0622	+	20.8923i	−0.413973	+	0.717022i
$850$		0			0
$851$	7.56218	+	13.0981i	0.259228	+	0.448996i
$852$		0			0
$853$	−31.9808			−1.09500			−0.547500	−	0.836806i	$-0.684420\pi$
$853$	−31.9808			−1.09500			−0.547500	+	0.836806i	$0.684420\pi$
$854$		0			0
$855$	−4.46410			−0.152669
$856$		0			0
$857$	−14.5622	−	25.2224i	−0.497435	−	0.861582i	0.502561	−	0.864542i	$-0.332391\pi$
$857$	−14.5622	−	25.2224i	−0.497435	−	0.861582i	−0.999996	+	0.00295983i	$0.999058\pi$
$858$		0			0
$859$	3.73205	−	6.46410i	0.127336	−	0.220552i	−0.795308	−	0.606206i	$-0.792691\pi$
$859$	3.73205	−	6.46410i	0.127336	−	0.220552i	0.922644	+	0.385654i	$0.126024\pi$
$860$		0			0
$861$	1.26795	−	1.46410i	0.0432116	−	0.0498964i
$862$		0			0
$863$	7.19615	−	12.4641i	0.244960	−	0.424283i	−0.717160	−	0.696908i	$-0.754559\pi$
$863$	7.19615	−	12.4641i	0.244960	−	0.424283i	0.962120	+	0.272625i	$0.0878919\pi$
$864$		0			0
$865$	−7.26795	−	12.5885i	−0.247118	−	0.428020i
$866$		0			0
$867$	−6.32051			−0.214656
$868$		0			0
$869$	−5.41154			−0.183574
$870$		0			0
$871$	−16.6244	−	28.7942i	−0.563295	−	0.975655i
$872$		0			0
$873$	−7.46410	+	12.9282i	−0.252622	+	0.437553i
$874$		0			0
$875$	−0.866025	−	2.50000i	−0.0292770	−	0.0845154i
$876$		0			0
$877$	2.07180	−	3.58846i	0.0699596	−	0.121174i	−0.828924	−	0.559362i	$-0.811046\pi$
$877$	2.07180	−	3.58846i	0.0699596	−	0.121174i	0.898883	+	0.438188i	$0.144380\pi$
$878$		0			0
$879$	−9.46410	−	16.3923i	−0.319216	−	0.552899i
$880$		0			0
$881$	9.85641			0.332071			0.166035	−	0.986120i	$-0.446903\pi$
$881$	9.85641			0.332071			0.166035	+	0.986120i	$0.446903\pi$
$882$		0			0
$883$	−53.5885			−1.80340			−0.901698	−	0.432367i	$-0.857678\pi$
$883$	−53.5885			−1.80340			−0.901698	+	0.432367i	$0.857678\pi$
$884$		0			0
$885$	−0.0980762	−	0.169873i	−0.00329680	−	0.00571022i
$886$		0			0
$887$	−12.6340	+	21.8827i	−0.424207	+	0.734749i	−0.996346	−	0.0854082i	$-0.972781\pi$
$887$	−12.6340	+	21.8827i	−0.424207	+	0.734749i	0.572139	+	0.820157i	$0.306114\pi$
$888$		0			0
$889$	4.16025	+	12.0096i	0.139530	+	0.402790i
$890$		0			0
$891$	0.366025	−	0.633975i	0.0122623	−	0.0212389i
$892$		0			0
$893$	−4.46410	−	7.73205i	−0.149385	−	0.258743i
$894$		0			0
$895$	10.0000			0.334263
$896$		0			0
$897$	10.7321			0.358333
$898$		0			0
$899$	0.973721	+	1.68653i	0.0324754	+	0.0562490i
$900$		0			0
$901$	−20.2487	+	35.0718i	−0.674582	+	1.16841i
$902$		0			0
$903$	5.53590	−	6.39230i	0.184223	−	0.212723i
$904$		0			0
$905$	12.1603	−	21.0622i	0.404221	−	0.700130i
$906$		0			0
$907$	16.7942	+	29.0885i	0.557643	+	0.965866i	0.997693	+	0.0678928i	$0.0216276\pi$
$907$	16.7942	+	29.0885i	0.557643	+	0.965866i	−0.440049	+	0.897974i	$0.645039\pi$
$908$		0			0
$909$	−7.26795			−0.241063
$910$		0			0
$911$	14.7321			0.488095			0.244047	−	0.969763i	$-0.421525\pi$
$911$	14.7321			0.488095			0.244047	+	0.969763i	$0.421525\pi$
$912$		0			0
$913$	−5.53590	−	9.58846i	−0.183211	−	0.317332i
$914$		0			0
$915$	−2.00000	+	3.46410i	−0.0661180	+	0.114520i
$916$		0			0
$917$	−40.1769	−	7.73205i	−1.32676	−	0.255335i
$918$		0			0
$919$	−15.4282	+	26.7224i	−0.508929	+	0.881492i	0.491017	+	0.871150i	$0.336625\pi$
$919$	−15.4282	+	26.7224i	−0.508929	+	0.881492i	−0.999947	+	0.0103417i	$0.996708\pi$
$920$		0			0
$921$	−16.0622	−	27.8205i	−0.529267	−	0.916717i
$922$		0			0
$923$	−14.0526			−0.462546
$924$		0			0
$925$	−3.19615			−0.105089
$926$		0			0
$927$	−4.59808	−	7.96410i	−0.151021	−	0.261575i
$928$		0			0
$929$	26.2224	−	45.4186i	0.860330	−	1.49014i	−0.0112804	−	0.999936i	$-0.503591\pi$
$929$	26.2224	−	45.4186i	0.860330	−	1.49014i	0.871611	−	0.490199i	$-0.163076\pi$
$930$		0			0
$931$	4.46410	+	30.9282i	0.146305	+	1.01363i
$932$		0			0
$933$	4.56218	−	7.90192i	0.149359	−	0.258697i
$934$		0			0
$935$	1.19615	+	2.07180i	0.0391184	+	0.0677550i
$936$		0			0
$937$	31.7321			1.03664			0.518320	−	0.855186i	$-0.326557\pi$
$937$	31.7321			1.03664			0.518320	+	0.855186i	$0.326557\pi$
$938$		0			0
$939$	−12.6603			−0.413152
$940$		0			0
$941$	15.0263	+	26.0263i	0.489843	+	0.848432i	0.999932	−	0.0116892i	$-0.00372087\pi$
$941$	15.0263	+	26.0263i	0.489843	+	0.848432i	−0.510089	+	0.860122i	$0.670388\pi$
$942$		0			0
$943$	1.73205	−	3.00000i	0.0564033	−	0.0976934i
$944$		0			0
$945$	2.59808	+	0.500000i	0.0845154	+	0.0162650i
$946$		0			0
$947$	−2.83013	+	4.90192i	−0.0919668	+	0.159291i	−0.908339	−	0.418235i	$-0.862649\pi$
$947$	−2.83013	+	4.90192i	−0.0919668	+	0.159291i	0.816372	+	0.577527i	$0.195982\pi$
$948$		0			0
$949$	−14.3564	−	24.8660i	−0.466029	−	0.807185i
$950$		0			0
$951$	−28.4449			−0.922388
$952$		0			0
$953$	−36.1051			−1.16956			−0.584780	−	0.811192i	$-0.698819\pi$
$953$	−36.1051			−1.16956			−0.584780	+	0.811192i	$0.698819\pi$
$954$		0			0
$955$	−4.46410	−	7.73205i	−0.144455	−	0.250203i
$956$		0			0
$957$	−1.53590	+	2.66025i	−0.0496485	+	0.0859938i
$958$		0			0
$959$	−3.80385	+	4.39230i	−0.122833	+	0.141835i
$960$		0			0
$961$	15.3923	−	26.6603i	0.496526	−	0.860008i
$962$		0			0
$963$	1.09808	+	1.90192i	0.0353850	+	0.0612886i
$964$		0			0
$965$	1.19615			0.0385055
$966$		0			0
$967$	10.1244			0.325577			0.162789	−	0.986661i	$-0.447951\pi$
$967$	10.1244			0.325577			0.162789	+	0.986661i	$0.447951\pi$
$968$		0			0
$969$	7.29423	+	12.6340i	0.234324	+	0.405862i
$970$		0			0
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$		0			0
$973$	5.13397	+	14.8205i	0.164588	+	0.475124i
$974$		0			0
$975$	−1.13397	+	1.96410i	−0.0363163	+	0.0629016i
$976$		0			0
$977$	8.29423	+	14.3660i	0.265356	+	0.459610i	0.967657	−	0.252270i	$-0.0811772\pi$
$977$	8.29423	+	14.3660i	0.265356	+	0.459610i	−0.702301	+	0.711880i	$0.747844\pi$
$978$		0			0
$979$	−11.0718			−0.353856
$980$		0			0
$981$	11.0000			0.351203
$982$		0			0
$983$	4.90192	+	8.49038i	0.156347	+	0.270801i	0.933549	−	0.358451i	$-0.116695\pi$
$983$	4.90192	+	8.49038i	0.156347	+	0.270801i	−0.777202	+	0.629252i	$0.783361\pi$
$984$		0			0
$985$	0.169873	−	0.294229i	0.00541260	−	0.00937490i
$986$		0			0
$987$	1.73205	+	5.00000i	0.0551318	+	0.159152i
$988$		0			0
$989$	7.56218	−	13.0981i	0.240463	−	0.416495i
$990$		0			0
$991$	−10.5526	−	18.2776i	−0.335213	−	0.580606i	0.648313	−	0.761374i	$-0.275475\pi$
$991$	−10.5526	−	18.2776i	−0.335213	−	0.580606i	−0.983526	+	0.180768i	$0.942142\pi$
$992$		0			0
$993$	−8.07180			−0.256151
$994$		0			0
$995$	−22.0000			−0.697447
$996$		0			0
$997$	27.9904	+	48.4808i	0.886464	+	1.53540i	0.844026	+	0.536302i	$0.180179\pi$
$997$	27.9904	+	48.4808i	0.886464	+	1.53540i	0.0424381	+	0.999099i	$0.486487\pi$
$998$		0			0
$999$	1.59808	−	2.76795i	0.0505609	−	0.0875740i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.o.961.1		4
4.3	odd	2		105.2.i.d.16.2	✓	4
7.4	even	3	inner	1680.2.bg.o.1201.1		4
12.11	even	2		315.2.j.c.226.1		4
20.3	even	4		525.2.r.a.499.1		4
20.7	even	4		525.2.r.f.499.2		4
20.19	odd	2		525.2.i.f.226.1		4
28.3	even	6		735.2.i.l.361.2		4
28.11	odd	6		105.2.i.d.46.2	yes	4
28.19	even	6		735.2.a.h.1.1		2
28.23	odd	6		735.2.a.g.1.1		2
28.27	even	2		735.2.i.l.226.2		4
84.11	even	6		315.2.j.c.46.1		4
84.23	even	6		2205.2.a.z.1.2		2
84.47	odd	6		2205.2.a.ba.1.2		2
140.19	even	6		3675.2.a.be.1.2		2
140.39	odd	6		525.2.i.f.151.1		4
140.67	even	12		525.2.r.a.424.1		4
140.79	odd	6		3675.2.a.bg.1.2		2
140.123	even	12		525.2.r.f.424.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.2	✓	4	4.3	odd	2
105.2.i.d.46.2	yes	4	28.11	odd	6
315.2.j.c.46.1		4	84.11	even	6
315.2.j.c.226.1		4	12.11	even	2
525.2.i.f.151.1		4	140.39	odd	6
525.2.i.f.226.1		4	20.19	odd	2
525.2.r.a.424.1		4	140.67	even	12
525.2.r.a.499.1		4	20.3	even	4
525.2.r.f.424.2		4	140.123	even	12
525.2.r.f.499.2		4	20.7	even	4
735.2.a.g.1.1		2	28.23	odd	6
735.2.a.h.1.1		2	28.19	even	6
735.2.i.l.226.2		4	28.27	even	2
735.2.i.l.361.2		4	28.3	even	6
1680.2.bg.o.961.1		4	1.1	even	1	trivial
1680.2.bg.o.1201.1		4	7.4	even	3	inner
2205.2.a.z.1.2		2	84.23	even	6
2205.2.a.ba.1.2		2	84.47	odd	6
3675.2.a.be.1.2		2	140.19	even	6
3675.2.a.bg.1.2		2	140.79	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-0.866025 - 2.50000i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(0.366025 + 0.633975i) q^{11} +2.26795 q^{13} +1.00000 q^{15} +(-1.63397 - 2.83013i) q^{17} +(2.23205 - 3.86603i) q^{19} +(-1.73205 + 2.00000i) q^{21} +(-2.36603 + 4.09808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} -4.19615 q^{29} +(-0.232051 - 0.401924i) q^{31} +(0.366025 - 0.633975i) q^{33} +(2.59808 + 0.500000i) q^{35} +(1.59808 - 2.76795i) q^{37} +(-1.13397 - 1.96410i) q^{39} -0.732051 q^{41} -3.19615 q^{43} +(-0.500000 - 0.866025i) q^{45} +(1.00000 - 1.73205i) q^{47} +(-5.50000 + 4.33013i) q^{49} +(-1.63397 + 2.83013i) q^{51} +(-6.19615 - 10.7321i) q^{53} -0.732051 q^{55} -4.46410 q^{57} +(-0.0980762 - 0.169873i) q^{59} +(-2.00000 + 3.46410i) q^{61} +(2.59808 + 0.500000i) q^{63} +(-1.13397 + 1.96410i) q^{65} +(-7.33013 - 12.6962i) q^{67} +4.73205 q^{69} -6.19615 q^{71} +(-6.33013 - 10.9641i) q^{73} +(-0.500000 + 0.866025i) q^{75} +(1.26795 - 1.46410i) q^{77} +(-3.69615 + 6.40192i) q^{79} +(-0.500000 - 0.866025i) q^{81} -15.1244 q^{83} +3.26795 q^{85} +(2.09808 + 3.63397i) q^{87} +(-7.56218 + 13.0981i) q^{89} +(-1.96410 - 5.66987i) q^{91} +(-0.232051 + 0.401924i) q^{93} +(2.23205 + 3.86603i) q^{95} +14.9282 q^{97} -0.732051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} + 16 q^{13} + 4 q^{15} - 10 q^{17} + 2 q^{19} - 6 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} + 6 q^{31} - 2 q^{33} - 4 q^{37} - 8 q^{39} + 4 q^{41} + 8 q^{43} - 2 q^{45} + 4 q^{47} - 22 q^{49} - 10 q^{51} - 4 q^{53} + 4 q^{55} - 4 q^{57} + 10 q^{59} - 8 q^{61} - 8 q^{65} - 12 q^{67} + 12 q^{69} - 4 q^{71} - 8 q^{73} - 2 q^{75} + 12 q^{77} + 6 q^{79} - 2 q^{81} - 12 q^{83} + 20 q^{85} - 2 q^{87} - 6 q^{89} + 6 q^{91} + 6 q^{93} + 2 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 - 2 * q^11 + 16 * q^13 + 4 * q^15 - 10 * q^17 + 2 * q^19 - 6 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 + 6 * q^31 - 2 * q^33 - 4 * q^37 - 8 * q^39 + 4 * q^41 + 8 * q^43 - 2 * q^45 + 4 * q^47 - 22 * q^49 - 10 * q^51 - 4 * q^53 + 4 * q^55 - 4 * q^57 + 10 * q^59 - 8 * q^61 - 8 * q^65 - 12 * q^67 + 12 * q^69 - 4 * q^71 - 8 * q^73 - 2 * q^75 + 12 * q^77 + 6 * q^79 - 2 * q^81 - 12 * q^83 + 20 * q^85 - 2 * q^87 - 6 * q^89 + 6 * q^91 + 6 * q^93 + 2 * q^95 + 32 * q^97 + 4 * q^99

Introduction

L-functions

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Database

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